In 2024, the National Center for Education Statistics (NCES) administered the National Assessment of Educational Progress (NAEP) mathematics assessment to representative samples of fourth- and eighth-grade students in the nation, states, the District of Columbia, Puerto Rico, Department of Defense schools, and 26 participating large urban…

The Individuals with Disabilities Education Act (IDEA) funds programs providing services designed to assist children with a range of delays and disabilities in achieving individualized developmental and functional goals. There are two types of programs. Part C Early Intervention is for children ages birth-2, and Part B Preschool is for children…

The Better Math Teaching Network offers a promising, practical model for teacher learning. Its practitioner members--who all teach at least one section of high school algebra and all joined voluntarily--are working with each other and a team of researchers to make their teaching more student-centered through an improvement science approach. With…

This report summarizes the results of the 2013-2014 AISD teacher appraisal and related survey items with emphasis on areas of need for additional professional development.

STEM Pathways aims to increase youths' long-term interest, learning, and achievement in STEM through a deliberate and interconnected system of STEM learning opportunities. In fall 2014 and spring 2015, a survey was administered to fourth- and fifth-grade students at the six STEM Pathways schools in Minneapolis Public Schools (MPS). Most of the…

Results from the Organisation for Economic Cooperation and Development's (OECD's) Programme for International Student Assessment (PISA) have shown that the degree to which education systems succeed in equipping students with important foundation skills varies significantly. Since the quality of teaching is at the heart of student learning…

Montgomery County Public Schools (MCPS) is more than a school system, it is a community. It's a community of people working together to provide Montgomery County students with an education that prepares them for success today, tomorrow, and in the years to come. That is MCPS' core purpose: to prepare students to thrive in their future. The Annual…

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

Maryland redesigned its CTE (career and technical education) program a dozen years ago to prepare students for the 21st Century's global economy and its rapidly changing workforce needs. With 350 business and industry representatives, the state created a program whose emphasis is problem-solving and critical thinking, rather than narrow,…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

Given a set of urns, each filled with a mix of black chips and white chips, what is the probability of drawing a black chip from the last urn after some sequential random shifts of chips among the urns? The Total Probability Formula (TPF) is the common tool to solve such a problem. However, when the number of urns is more than two and the number…

The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…